August  2008, 21(3): 703-716. doi: 10.3934/dcds.2008.21.703

Convergence to self-similar solutions for a semilinear parabolic equation

1. 

Department of Applied Mathematics and Statistics, Comenius University, 842 48 Bratislava

2. 

Department of Mathematics I, Wüllnerstr. 5-7, RWTH Aachen, 52056 Aachen

3. 

Mathematical Institute, Tohoku University, Sendai 980-8578

Received  May 2007 Revised  February 2008 Published  April 2008

We study the behavior of solutions of the Cauchy problem for a parabolic equation with power nonlinearity. Our concern is the rate of convergence of solutions to forward self-similar solutions. We determine the exact rate of convergence which turns out to depend on the spatial decay rate of initial data.
Citation: Marek Fila, Michael Winkler, Eiji Yanagida. Convergence to self-similar solutions for a semilinear parabolic equation. Discrete & Continuous Dynamical Systems - A, 2008, 21 (3) : 703-716. doi: 10.3934/dcds.2008.21.703
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